Chapter 9.8, Problem 7CYU

(a)

To determine

To calculate: To graph the equation and to find the height of the ball after $2$ seconds.

Answer to Problem 7CYU

The height of the ball after $2$ seconds is $18$

Explanation of Solution

Given information: A soccer ball is kicked straight up into the air. The height of the ball $h$ after $t$ seconds can be modeled by the equation $h=-16t^2+40t+2$

Calculation:

Given that the height of the ball $h$ after $t$ seconds can be modeled by the equation

  $h=-16t^2+40t+2$

In order to graph the equation, find the solutions of the equation

When $t=0$

  $\begin{array}{l}h=-16{\left(0\right)}^2+40\left(0\right)+2\\ h=2\end{array}$

When $t=1$

  $\begin{array}{l}h=-16{\left(1\right)}^2+40\left(1\right)+2\\ h=-16+42\\ h=26\end{array}$

When $t=2$

  $\begin{array}{l}h=-16{\left(2\right)}^2+40\left(2\right)+2\\ h=-16\left(4\right)+80+2\\ h=-64+82\\ h=18\end{array}$

When $t=3$

  $\begin{array}{l}h=-16{\left(3\right)}^2+40\left(3\right)+2\\ h=-16\left(9\right)+120+2\\ h=-144+122\\ h=-22\end{array}$

Plotting the points on graph:

  

Height of the ball after $2$ seconds is calculated by substituting $t=2$ in the equation:

  $\begin{array}{l}h=-16{\left(2\right)}^2+40\left(2\right)+2\\ h=-16\left(4\right)+80+2\\ h=-64+82\\ h=18\end{array}$

Conclusion:

Hence, height of the ball after $2$ seconds is $18$

(b)

To determine

To calculate: To find the value of domain and range are unreasonable

Answer to Problem 7CYU

Domain is $\left[0,2.5\right]$

Range is $\left[0,27\right]$

Explanation of Solution

Given information: A soccer ball is kicked straight up into the air. The height of the ball $h$ after $t$ seconds can be modeled by the equation $h=-16t^2+40t+2$

Calculation:

Given that the height of the ball $h$ after $t$ seconds can be modeled by the equation

  $h=-16t^2+40t+2$

Graph of the function is as follows

  

From the graph,

Domain is $\left[0,2.5\right]$

Range is $\left[0,27\right]$

Conclusion:

Hence, Domain is $\left[0,2.5\right]$

Range is $\left[0,27\right]$